1. Field of the Invention
The invention relates to digital communication systems. It is particularly applicable to communication systems where data is transmitted over a time-variant or frequency-variant channel, such as in mobile communication systems or satellite communication.
2. Description of the Related Art
For transmission over long distances or wireless links, digital data is modulated onto one or more carriers. Various modulation schemes are known in prior art, such as amplitude shift keying (ASK), phase shift keying (PSK) and mixed amplitude and phase modulation like quadrature amplitude modulation, QAM. In all mentioned modulation types, the modulated signal, in terms of for example voltage or field strength, can be expressed byu=(t)=Re(A·ejωt)
A bit sequence, or data word, is represented by a complex value A, wherein|A|=√{square root over (Re(A)2+(Im(A)2)}{square root over (Re(A)2+(Im(A)2)}represents the momentary amplitude of the modulated signal andφ(A)=arctan(Im(A)/Re(A))represents the momentary phase of the modulated signal. The assignment between values of the bit sequence and complex values is called mapping.
As real transmission channels distort the modulated signal by phase shift and attenuation, and as they add noise to the signal, errors occur in the received data after demodulation. The probability for errors usually rises with rising data rate, that is with rising number of modulation states and falling symbol duration. To cope with such errors, redundancy can be added to the data, which allows to recognise and to correct erroneous symbols. A more economic approach is given by methods which repeat only the transmission of data in which un-correctable errors have occurred, such as hybrid automatic repeat request, HARQ, and incremental redundancy.
EP 1 293 059 B1 shows a method to rearrange digital modulation symbols in order to improve the mean reliabilities of all bits. This is achievable by changing the mapping rule of bits onto symbols. This patent focuses on the rearrangement for retransmitted symbols in an ARQ system.
EP 1 313 250 A1 and EP 1 313 251 A1 give a mechanism how the effect of EP 1 293 059 B1 can be achieved by using the same mapping rule of bits onto symbols and instead manipulating the bits prior to the mapping by interleaving and/or logical bit inversion operations. These methods are also restricted on ARQ systems.
WO 2004 036 817 and WO 2004 036 818 describe how to achieve the reliability averaging effect for a system where an original and a repeated symbol are transmitted over different diversity branches, or in combination with an ARQ system.
The methods and mechanisms of the patent publications cited above will be referred to as “Constellation Rearrangement” or “CoRe” for simplicity.
A major difference between wired communication systems and wireless communication systems is the behaviour of the physical channel over which information is transmitted. The wireless or mobile channel is by its very nature variant over time and/or frequency. For a good performance in most modern mobile communication systems a demodulation of data symbols in a receiver requires an accurate estimation of the channel, usually measured by a channel coefficient, which includes knowledge about the power, the phase, or both properties of the channel. To facilitate this, usually some sort of pilot symbols are inserted into the data symbol stream which have a predetermined unambiguous amplitude and/or phase value, which can be used to determine the channel coefficient. This information is then used for correction measures like adaptive filtering.
“Decision-Feedback Demodulation” is an iterative process where a first rough channel estimate (or none at all) is used to demodulate the data symbols. After demodulation, and preferably after decoding, the obtained information is fed back to the channel estimator for an improved estimation resulting from the data symbols. It should be apparent that this process causes not only delay and requires a lot of computations in each iteration step, but it also depends greatly on the quality of the first rough channel estimate due to the feedback loop. Such procedure is known for example from Lutz H.-J. Lampe and Robert Schober, “Iterative Decision-Feedback Differential Demodulation of Bit-interleaved Coded MDPSK for Flat Rayleigh Fading Channels”.
Usually the data symbols themselves cannot be accurately used for channel estimation, since the amplitude and/or phase are not known a priori to demodulation. The receiver has to conclude on a sent symbol based on the received signal, before channel estimation is possible. As the recognition of the symbol might be erroneous, ambiguity is introduced to the channel estimation. This behaviour can be seen from FIG. 1 and is further detailed in Table 1 to show the number of ambiguities involved in different digital modulation schemes.
TABLE 1Properties of selected digital modulation methodsBits perModulation SchemeSymbolAmplitude AmbiguityPhase AmbiguityBPSK1None/1 Level2 LevelsQPSK2None/1 Level4 Levels8-PSK3None/1 Level8 Levels2-ASK/4-PSK32 Levels4 Levels4-ASK/2-PSK34 Levels2 Levels8-ASK38 LevelsNone/1 Level16-PSK4None/1 Level16 Levels 16-QAM43 Levels12 Levels 4-ASK/4-PSK44 Levels4 Levels64-QAM69 Levels52 Levels 
From Table 1 it follows also easily that the performance of an iterative decision-feedback demodulation scheme will further depend greatly on the number of ambiguities involved in the modulation scheme. A wrong assumption about the sent symbol leads to a wrong result of the channel estimation. Especially in modulation schemes with a high number of modulation states there is a high probability of erroneous symbols due to inevitable noise. A wrong channel estimation, in turn, leads to wrong correction and consequently more errors in received symbols. Therefore there is a need in the related art for improved reliability of the channel estimation.
The above-mentioned prior art addresses only the aspect of averaging the mean bit reliabilities of bits that are mapped onto one digital symbol by rearranging the mappings or by bit operations prior to mapping. While this has a good effect if the time-/frequency-variant channel is known very accurately, it does not provide means to improve the knowledge of the time-/frequency-variant channel at the receiver if the coherence time/frequency is relatively small compared to a data packet.
Gray Mapping or Gray Coding are terms that are widely used in communication systems when digital modulation is used, therefore the description here is very basic. A Gray Mapping is characterized by the fact that the XOR binary operation on the bit sequence of a first symbol and the bit sequence of a nearest-neighbouring second symbol in the complex signal plane has a Hamming weight of 1, i.e. that the results of the XOR results in a binary word which contains the bit value 1 exactly a single time. In other words, in a Gray mapping, bit sequences assigned to closest neighbours differ only in the value of (any) one bit.
Here is one algorithm to convert from “natural binary codes” to Gray code for a one-dimensional arrangement:                Let B[n:0] the array of bits in the usual binary representation (e.g. binary 1101 for decimal 13)        Let G[n:0] the array of bits in Gray code        G[n]=B[n]        for i=n−1 down to i=0: G[i]=B[i+1] XOR B[i]        
Another recursive generation method is the following:
The Gray code for n bits can be generated recursively by prefixing a binary 0 to the Gray code for n−1 bits, then prefixing a binary 1 to the reflected (i.e. listed in reverse order) Gray code for n−1 bits. This is shown for 1 to 4 bits in FIG. 26.
In two-dimensional arrangement like a mapping of binary numbers to modulation states of a quadrature amplitude modulation (QAM), when the bits of which the numbers consist can be separated into different sub-sets characterising the position with respect to different dimensions, a Gray mapping may be obtained by applying the method above to each of the sub-sets separately. Commonly the result is such that the Gray principle holds in the two-dimensional arrangement only with respect to the nearest neighbour(s) of a constellation point.